Re: [Discuss-gnuradio] USRP complex multiplication question

[Nick Foster]

On Wed, 2011-05-25 at 12:14 -0500, John Andrews wrote:
> Dear All,
> 
> I have a question regarding the first complex multiplication process
> with the IF sinusoid in the USRP. Which of the scheme mentioned below
> is actually happening in the USRP?

I should also clarify -- USRPs are zero-IF quadrature receivers
(excepting the TVRX daughterboards). The daughterboards (excepting the
TVRX series) have quadrature outputs and send complex baseband signals
to the two ADCs.

--n

> 
> 
> Let's say that two ADCs provide the sampled received signal to the
> next stage of processing. Let's call the sampled stream of ADC_0 as A
> and sampled stream of ADC_1 as B.
> 
> 
> 
> 
> SCHEME-1
> 
> 
> The NCO produces two sinusoids that are in quadrature phase with each
> other. These are sin(2*pi*f*t) and cos(2*pi*f*t). Let's call the
> sin(2*pi*f*t)stream as C and
> cos(2*pi*f*t) stream as D. The multiplier after the ADC stage does the
> following.
> 
> 
> 1. Multiplies the cos(2*pi*fc*t) stream, C,  with the sampled data
> stream of ADC_0, which is the stream named A and the product is AC.
> 2. Multiplies the sin(2*pi*fc*t) stream with the sampled data stream
> of ADC_1, which is the stream named B and the product is BD.
> 
> 
> Then sends the resultant product  from these two steps as a complex
> sample, ( AC + jBD ) 
> 
> 
> SCHEME-2
> 
> 
> The NCO produces two sinusoids that are in quadrature phase with each
> other. These are sin(2*pi*f*t) and cos(2*pi*f*t). The multiplier after
> the ADC stage does the following.
> 
> 
> The multiplier after ADC stage then multiplies the ADC outputs with
> the NCO outputs as
> ( A + jB ) * ( C + jD) = (AC - BD) + j(AD + BC)
> and sends the above output as a complex sample. 
> 
> 
> Which one is true?
> 
> 
> Thanks
> 
> 
> 
> 
> 
> 
> 
> 
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